Estimates Of Model Parameters Research Articles

A temporal assessment of distracted driving injury severities using alternate unobserved-heterogeneity modeling approaches

This study explores temporal shifts in the effects of explanatory variables on the injury severity outcomes of crashes involving distracted driving. Using data from distracted driving crashes on Kansas State highways over a four-year period (from 2014 to 2017 inclusive), separate yearly models of driver-injury severities (with possible outcomes of severe injury, minor injury, and no injury) were estimated using two alternate modeling approaches to account for possible unobserved heterogeneity: a latent-class multinomial logit with class probability functions and a random parameters logit with possible heterogeneity in the means and variances of random parameters. Likelihood ratio tests were conducted to determine if model parameter estimates have shifted over time. A wide range of variables were found to statistically influence driver-injury severities and the findings show that were statistically significant temporal shifts in parameter estimates in both the random parameters and latent class modeling approaches. These shifts are likely the result of changes in driver behavior, improvements in vehicle and highway safety features, changes in communication technologies, and other temporally shifting trends. However, while out-of-sample simulations show that the two modeling approaches both indicate that distracted driving crashes have become less severe over time, the alternate approaches produced substantially different injury-severity predictions, suggesting the need for future research to explore how unobserved heterogeneity can best be modeled in temporal contexts.

Predicting the time to detect moderately virulent African swine fever virus in finisher swine herds using a stochastic disease transmission model

BackgroundAfrican swine fever (ASF) is a highly contagious and devastating pig disease that has caused extensive global economic losses. Understanding ASF virus (ASFV) transmission dynamics within a herd is necessary in order to prepare for and respond to an outbreak in the United States. Although the transmission parameters for the highly virulent ASF strains have been estimated in several articles, there are relatively few studies focused on moderately virulent strains. Using an approximate Bayesian computation algorithm in conjunction with Monte Carlo simulation, we have estimated the adequate contact rate for moderately virulent ASFV strains and determined the statistical distributions for the durations of mild and severe clinical signs using individual, pig-level data. A discrete individual based disease transmission model was then used to estimate the time to detect ASF infection based on increased mild clinical signs, severe clinical signs, or daily mortality.ResultsOur results indicate that it may take two weeks or longer to detect ASF in a finisher swine herd via mild clinical signs or increased mortality beyond levels expected in routine production. A key factor contributing to the extended time to detect ASF in a herd is the fairly long latently infected period for an individual pig (mean 4.5, 95% P.I., 2.4 - 7.2 days).ConclusionThese transmission model parameter estimates and estimated time to detection via clinical signs provide valuable information that can be used not only to support emergency preparedness but also to inform other simulation models of evaluating regional disease spread.

Convexity and Feedback in Approximate Dynamic Programming for Delivery Time Slot Pricing

We consider the revenue management problem of finding profit-maximizing prices for delivery time slots in the context of attended home delivery. This multistage optimal control problem admits a dynamic programming (DP) formulation that is intractable for realistic problem sizes due to the so-called “curse of dimensionality.” We therefore study three approximate DP algorithms both from a numerical and control-theoretical perspective. Our analysis is based on real-world data, from which we generate multiple scenarios to stress-test the robustness of the pricing policies to errors in model parameter estimates. Our theoretical analysis and numerical benchmark tests indicate that one of these algorithms, namely gradient-bounded DP, dominates the others with respect to computation time and profit-generation capabilities of the pricing policies that it generates.

Reversible Jump MCMC Algorithm for Transformed Laplacian AR: Application in Modeling CO<sub>2</sub> Emission Data

Autoregressive (AR) model is applied to model various types of data. For confidential data, data confusion is very important to protect the data from being known by other unauthorized parties. This paper aims to find data modeling with transformations in the AR model. In this AR model, the noise has a Laplace distribution. AR model parameters include order, coefficients, and variance of the noise. The estimation of the AR model parameter is proposed in a Bayesian method by using the reversible jump Markov Chain Monte Carlo (MCMC) algorithm. This paper shows that the posterior distribution of AR model parameters has a complicated equation, so the Bayes estimator cannot be determined analytically. Bayes estimators for AR model parameters are calculated using the reversible jump MCMC algorithm. This algorithm was validated through a simulation study. This algorithm can accurately estimate the parameters of the transformed AR model with Laplacian noise. This algorithm produces an AR model that satisfies the stationary conditions. The novelty in this paper is the use of transformations in the Laplacian AR model to secure research data when the research results are published in a scientific journal. As an example application, the Laplacian AR model was used to model CO₂ emission data. The results of this paper can be applied to modeling and forecasting confidential data in various sectors.

Estimation of the parameters of the gamma geometric process

There is no doubt that finding the estimators of model parameters accurately and efficiently is very important in many fields. In this study, we obtain the explicit estimators of the unknown model parameters in the gamma geometric process (GP) via the modified maximum likelihood (MML) methodology. These estimators are as efficient as maximum likelihood (ML) estimators. The marginal and joint asymptotic distributions of the MML estimators are also derived and efficiency comparisons between ML and MML estimators are made through an extensive Monte Carlo simulations. Moreover, a real data example is considered to illustrate the performances of the MML estimators together with their ML counterparts. According to simulation results, the performances of MML and ML estimators are close to each other even for small sample sizes.

Modeling COVID-19 Data with a Novel Extended Exponentiated Class of Distributions

The COVID-19 epidemic has affected every aspect of daily life since December 2019 and caused massive damage to the world. The coronavirus epidemic has affected more than 150 countries around the world. Many researchers have tried to develop a statistical model which can be utilized to analyze the behavior of the COVID-19 data. This article contributes to the field of probability theory by introducing a novel family of distributions, named the novel extended exponentiated class of distributions. Explicit expressions for numerous mathematical characterizations of the proposed family have been obtained with special concentration on a three-parameter submodel of the new class of distributions, named the new extended exponentiated Weibull distribution. The unknown model parameter estimates are obtained via the maximum likelihood estimation method. To assess the performance of these estimates, a comprehensive simulation study is conducted. Three different sets of COVID-19 data are used to check the applicability of the submodel case. The submodel of the new family is compared with three well-known probability distributions. Using different analytical measures, the results demonstrate that the new extended exponentiated Weibull distribution gives promising results in terms of its flexibility and offers data modeling with increasing decreasing, unimodal, and modified unimodal shapes.

The effects of student s gender and classroom disruptive behaviors and parental income on student s mathematics achievement trajectory

The goal of the study was to examine the role of students’ gender, their disruptive behaviors, and parental income on their mathematics achievement history. Participants included 8,984 individuals aged 12-16 years and the data were collected from the National Longitudinal Surveys (NLS). The study results showed that there was not any significant gender effect on students’ mathematics achievement trajectories. Furthermore, students with disruptive behaviors were more successful than their peers with less disruptive behaviors. Finally, the latent growth curve model parameter estimates indicated there was not any significant parental earned income impact on students’ mathematics achievement trajectories.

Estimating the natural mortality rate of saucer scallops (Ylistrum balloti) on the Queensland east coast from tag-recaptures

Saucer scallops (Ylistrum balloti) were tagged and released on four occasions inside two areas closed to fishing (Hervey Bay A, HBA; and Yeppoon B, YB) on the Queensland (Australia) east coast and their subsequent recaptures over the following months were used to measure the instantaneous rate of natural mortality (M). A total of 13,295 scallops were tagged and 526 recaptured over the 15 month-long experiment (May 2018 to August 2019). Three statistical approaches were applied to the experimental design and analysis of the tagging data, based on 1) the Brownie model, 2) a modified version of the Brownie model, and 3) a binomial logistic regression model of recaptures. Estimates of M based on the Brownie model were much higher for tagged scallops that were at liberty over summer months compared to those at liberty over the winter months, possibly indicating seasonal variation. The logistic model parameter estimates indicated the proportion of recaptures differed significantly with the lunar phase at recapture, scallop size class, the number of days the scallops were at liberty and the interaction between days-at-liberty and closure. All three approaches indicated M was higher in HBA compared to YB. Mean estimates of M for the whole fishery, derived by averaging estimates from both closures, ranged from a minimum of 1.461 year–1 for the logistic model, to 1.501 year–1 for the Brownie model, to 1.548 year–1 (variable recapture rate) and 1.594 year–1 (fixed recapture rate) for the modified Brownie model. Estimates from all three approaches were higher than the previous estimate that was published over 40 years ago and possible reasons for the increase are discussed.

Watch-and-Wait policy versus robotic surgery for locally advanced rectal cancer: A cost-effectiveness study (RECCOSTE)

IntroductionComplete surgical resection for locally advanced rectal cancer is the standard treatment after a clinical complete response following chemoradiotherapy. However, some novel clinical approaches could achieve better functional results, such as Robotic Resection, or avoiding surgical procedure and incrementing surveillance intensity, called Watch-and-Wait policy. We use computational techniques to compare these clinical approaches using quality adjusted life years (QALYs). MethodsA Markov decision analytic model was used in order to perform a cost-utility analysis, comparing standard resection (SR), Robotic Rectal Resection (RRR) and Watch-and-Wait (WW) strategies, estimating the incremental cost-effectiveness ratio per QALY to be gained from patients reaching a clinical complete response to chemoradiotherapy. Model parameter estimates were informed by previously published studies comparing WW to SR and from our database of RRR versus SR. Lifetime incremental cost-utility ratio was calculated among approaches, and a sensitivity analysis were performed in order to estimate the model uncertainty. A willingness-to-pay of per one additional QALY gained was measured to determine which strategies would be most cost-effective. ResultsWW is a dominating option over SR ( -75,486. 75 € and +2.04 QALYs) and RRR ( -75,486. 75 € and +0.41 QALYs). The cost-effectiveness plane shows that WW does not always dominate over RRR or SR. WW saves costs in 99.98% of the simulations when compared with either SR or RRR but only 86.9% and 55.38% (respectively) of these fall within the SR quadrant. WW is only more effective than SR 55% of the time which implies a significant uncertainty due to the high utility value assigned to cCR after chemoradiotherapy in the RRR alternative. ConclusionThis study provides data of cost-effectiveness differences among Standard Surgery, Watch-and-Wait and Robotic Resection approaches in clinical complete response in locally advanced rectal cancer patients after neoadjuvant chemoradiotherapy, showing a benefit for Watch-and-Wait policy.

Data assimilation of volcanic aerosol observations using FALL3D+PDAF

Abstract. Modelling atmospheric dispersal of volcanic ash and aerosols is becoming increasingly valuable for assessing the potential impacts of explosive volcanic eruptions on buildings, air quality, and aviation. Management of volcanic risk and reduction of aviation impacts can strongly benefit from quantitative forecasting of volcanic ash. However, an accurate prediction of volcanic aerosol concentrations using numerical modelling relies on proper estimations of multiple model parameters which are prone to errors. Uncertainties in key parameters such as eruption column height and physical properties of particles or meteorological fields represent a major source of error affecting the forecast quality. The availability of near-real-time geostationary satellite observations with high spatial and temporal resolutions provides the opportunity to improve forecasts in an operational context by incorporating observations into numerical models. Specifically, ensemble-based filters aim at converting a prior ensemble of system states into an analysis ensemble by assimilating a set of noisy observations. Previous studies dealing with volcanic ash transport have demonstrated that a significant improvement of forecast skill can be achieved by this approach. In this work, we present a new implementation of an ensemble-based data assimilation (DA) method coupling the FALL3D dispersal model and the Parallel Data Assimilation Framework (PDAF). The FALL3D+PDAF system runs in parallel, supports online-coupled DA, and can be efficiently integrated into operational workflows by exploiting high-performance computing (HPC) resources. Two numerical experiments are considered: (i) a twin experiment using an incomplete dataset of synthetic observations of volcanic ash and (ii) an experiment based on the 2019 Raikoke eruption using real observations of SO2 mass loading. An ensemble-based Kalman filtering technique based on the local ensemble transform Kalman filter (LETKF) is used to assimilate satellite-retrieved data of column mass loading. We show that this procedure may lead to nonphysical solutions and, consequently, conclude that LETKF is not the best approach for the assimilation of volcanic aerosols. However, we find that a truncated state constructed from the LETKF solution approaches the real solution after a few assimilation cycles, yielding a dramatic improvement of forecast quality when compared to simulations without assimilation.

A flow-diffusion model of oxygen transport for quantitative mapping of cerebral metabolic rate of oxygen (CMRO2) with single gas calibrated fMRI

One promising approach for mapping CMRO2 is dual-calibrated functional MRI (dc-fMRI). This method exploits the Fick Principle to combine estimates of CBF from ASL, and OEF derived from BOLD-ASL measurements during arterial O2 and CO2 modulations. Multiple gas modulations are required to decouple OEF and deoxyhemoglobin-sensitive blood volume. We propose an alternative single gas calibrated fMRI framework, integrating a model of oxygen transport, that links blood volume and CBF to OEF and creates a mapping between the maximum BOLD signal, CBF and OEF (and CMRO2). Simulations demonstrated the method’s viability within physiological ranges of mitochondrial oxygen pressure, PmO2, and mean capillary transit time. A dc-fMRI experiment, performed on 20 healthy subjects using O2 and CO2 challenges, was used to validate the approach. The validation conveyed expected estimates of model parameters (e.g., low PmO2), with spatially uniform OEF maps (grey matter, GM, OEF spatial standard deviation ≈ 0.13). GM OEF estimates obtained with hypercapnia calibrated fMRI correlated with dc-fMRI (r = 0.65, p = 2·10−3). For 12 subjects, OEF measured with dc-fMRI and the single gas calibration method were correlated with whole-brain OEF derived from phase measures in the superior sagittal sinus (r = 0.58, p = 0.048; r = 0.64, p = 0.025 respectively). Simplified calibrated fMRI using hypercapnia holds promise for clinical application.

A semi-parametric, state-space compartmental model with time-dependent parameters for forecasting COVID-19 cases, hospitalizations and deaths.

Short-term forecasts of the dynamics of coronavirus disease 2019 (COVID-19) in the period up to its decline following mass vaccination was a task that received much attention but proved difficult to do with high accuracy. However, the availability of standardized forecasts and versioned datasets from this period allows for continued work in this area. Here, we introduce the Gaussian infection state space with time dependence (GISST) forecasting model. We evaluate its performance in one to four weeks ahead forecasts of COVID-19 cases, hospital admissions and deaths in the state of California made with official reports of COVID-19, Google’s mobility reports and vaccination data available each week. Evaluation of these forecasts with a weighted interval score shows them to consistently outperform a naive baseline forecast and often score closer to or better than a high-performing ensemble forecaster. The GISST model also provides parameter estimates for a compartmental model of COVID-19 dynamics, includes a regression submodel for the transmission rate and allows for parameters to vary over time according to a random walk. GISST provides a novel, balanced combination of computational efficiency, model interpretability and applicability to large multivariate datasets that may prove useful in improving the accuracy of infectious disease forecasts.

Gaussian copula joint models for mixed longitudinal zero-inflated count and continuous responses

Gaussian copula joint models for mixed correlated longitudinal continuous and count responses with random effects are presented where the count responses have zero-inflated power series distribution. To account for associations between zero-inflated count and continuous responses, we use the Gaussian copula to indirectly specify their joint distributions. A full likelihood-based approach is applied to obtain IFM method to estimate marginal parameters marginally and share parameters jointly. In this method, we used the Monte Carlo EM algorithm to obtain the parameter estimates of Gaussian copula joint models. To illustrate the utility of the models, some simulation studies are performed. Finally, the proposed models are motivated by applying a medical data set. The data set is extracted from an observational study where the correlated responses are the continuous response of body mass index and the power series response of the number of joint damages.

Investigating the barriers that intensify undergraduates’ unwillingness to online learning during COVID-19: A study on public universities in a developing country

Online learning has been extensively conducted to continue the academic activities in the universities transversely the realm during the pandemic instigated by COVID-19. Like other countries’ universities across the world, universities in a developing country such as Bangladesh are going through the online learning phenomenon. However, the current virtual platform of learning implies enormous challenges for undergraduates to participate in the online learning process due to numerous barriers. Thus, the current paper intends to examine barriers that intensify unwillingness to online education at the university level in the context of Bangladesh. Based on the underpinning theories of TAM3 and UTAUT, this study identified four major barriers such as financial, insufficient institutional support, technological, and individual. Furthermore, gender is considered as moderating variable in the model. To inspect such barriers along with the moderating variable, this study employs the Partial Least Squares (PLS) technique to estimate the measurement and structural model parameters and to generate the coexisting bootstrap assessments. The bootstrapping procedure has been initiated to test the statistical significance of the model parameter estimations. The findings confirm that technological, and insufficient institutional support barriers are statistically significant whereas the other two barriers have been revealed as non-significant to intensify learners’ reluctance to the online study. Furthermore, current findings also ratify no significant effect of gender as a moderating variable. Finally, this study augments specific policy implications for diverse stakeholders in current settings.

Limits of Accuracy for Parameter Estimation and Localization in Single-Molecule Microscopy via Sequential Monte Carlo Methods

Assessing the quality of parameter estimates for models describing the motion of single molecules in cellular environments is an important problem in fluorescence microscopy. In this work, we consider the fundamental data model, where molecules emit photons at random time instances and these photons arrive at random locations on the detector according to complex point spread functions (PSFs). The randomness and non-Gaussian PSF of the detection process, and the random trajectory of the molecule, make inference challenging. Moreover, the presence of other closely spaced molecules causes further uncertainty in the origin of the measurements, which impacts the statistical precision of the estimates. We quantify the limits of accuracy of model parameter estimates and separation distance between closely spaced molecules (known as the resolution problem) by computing the Cramér--Rao lower bound (CRLB), or equivalently the inverse of the Fisher information matrix (FIM), for the variance of estimates. Results on the CRLB obtained from the fundamental model are crucial, in that they provide a lower bound for more practical scenarios. While analytic expressions for the FIM can be derived for static and deterministically moving molecules, the analytical tools to evaluate the FIM for molecules whose trajectories follow stochastic differential equations are still for the most part missing. We address this by presenting a general sequential Monte Carlo (SMC) based methodology for both parameter inference and computing the desired accuracy limits for nonstatic molecules and a non-Gaussian fundamental detection model. For the first time, we are able to estimate the FIM for stochastically moving molecules observed through the Airy and Born and Wolf detection models. This is achieved by estimating the score and observed information matrix via SMC. We summarize the outcome of our numerical work by delineating the qualitative behaviors for the accuracy limits as functions of various experimental settings like collected photon count, molecule diffusion, etc. We also verify that we can recover known results from the static molecule case.

A New Family of Distributions Based on Proportional Hazards

In this article, we introduce a new family of symmetric-asymmetric distributions based on skew distributions and on the family of order statistics with proportional hazards. This new family of distributions is able to fit both unimodal and bimodal asymmetric data. Furthermore, it contains, as special cases, the symmetric distribution and the “skew-symmetric” family, and therefore the skew-normal distribution. Another interesting feature of the family is that the parameter controlling the distributional shape in bimodal cases takes values in the interval (0, 1); this is an advantage for computing maximum likelihood estimates of model parameters, which is performed by numerical methods. The practical utility of the proposed distribution is illustrated in two real data applications.

Parsimonious mixture‐of‐experts based on mean mixture of multivariate normal distributions

The mixture‐of‐experts (MoE) paradigm attempts to learn complex models by combining several “experts” via probabilistic mixture models. Each expert in the MoE model handles a small area of the data space in which a gating function controls the data‐to‐expert assignment. The MoE framework has been used extensively in designing non‐linear models in machine learning and statistics to model the heterogeneity in data for the purpose of regression, classification and clustering. The existing MoE of multi‐target regression (MoE‐MTR) models for continuous data is based on multivariate normal distributions. However, in many practical situations, for a set of data, a group or groups of observations may exhibit asymmetric and heavy‐tailed behaviour, and inference based on symmetric distributions in such situations can unduly affect the fit of the regression model. We introduce here a novel robust multivariate non‐normal MoE model by the use of mean mixture of normal distributions. The proposed model can handle the issues of MoE‐MTR models regarding possibly skewed, heavy‐tailed and noisy data. Maximum likelihood estimates of model parameters are developed based on an expectation‐maximization (EM)‐type algorithm. Parsimony is also obtained by imposing suitable constraints on the expert dispersion matrices. The usefulness of the proposed methodology is illustrated using simulated and real data sets.

Risk mitigation in model-based experiment design: A continuous-effort approach to optimal campaigns

A key challenge in maximizing the effectiveness of model-based design of experiments for calibrating nonlinear process models is the inaccurate prediction of information that is afforded by each new experiment. We present a novel methodology to exploit prior probability distributions of model parameter estimates in a bi-objective optimization formulation, where a conditional-value-at-risk criterion is considered alongside an average information criterion. We implement a tractable numerical approach that discretizes the experimental design space and leverages the concept of continuous-effort experimental designs in a convex optimization formulation. We demonstrate effectiveness and tractability through three case studies, including the design of dynamic experiments. In one case, the Pareto frontier comprises experimental campaigns that significantly increase the information content in the worst-case scenarios. In another case, the same campaign is proven to be optimal irrespective of the risk attitude. An open-source implementation of the methodology is made available in the Python software Pydex.

Joint parameter-input estimation for virtual sensing on an offshore platform using output-only measurements

This paper presents a recursive Bayesian inference framework for joint parameter-input identification, and virtual sensing for strain time history prediction of an offshore platform using sparse output-only measurements. The studied offshore platform, known as FINO3, is in the North Sea and is instrumented with a variety of sensors, including accelerometers and strain gauges. Offshore platforms are fatigue critical structures due to harsh marine environmental conditions and continuous cyclic wind and wave loads. Therefore, continuous monitoring of strain time histories at hotspot locations of offshore structures is important for reducing maintenance cost and avoiding unexpected failures. A windowed unscented Kalman filter (UKF) is employed to estimate an uncertain modeling parameter (foundation stiffness) and unknown input load time histories using output-only acceleration and strain measurements. The input loads are divided into overlapping windows, and windowed inputs and model parameters are combined as an augmented state vector in the UKF framework. Then strain time histories at critical locations are estimated through a virtual sensing strategy using the estimated input loads and model parameter. A traditional modal expansion approach combined with model updating is also implemented for the purpose of verification and comparison. The proposed method is first demonstrated through a numerical study using a finite element model of FINO3, where accurate model parameter and input estimations are obtained. Then the approach is further investigated using the actual measurements on FINO3. More accurate strain predictions are provided by the UKF than the modal expansion approach, which recommends the proposed UKF method for fatigue monitoring and input estimation.

Fitting Volume Models for Parana Pine With a Nonlinear Regression, Genetic Algorithm and Simulated Annealing

Improving volumetric quantification of Parana pine (Araucaria angustifolia) in Mixed Ombrophilous Forest is a constant need in order to provide accurate and timely information on current and future growing stock to ensure forest management. Thus, the present study aimed to evaluate and compare the volume estimates obtained through Nonlinear Regression (NR), Genetic Algorithm (GA) and Simulated Annealing (SA) in order to generate accurate volume estimates. Volumetric equations were developed including the independent variables diameter at breast height (dbh), total height (h) and crown rate (cr) and from the fit through the NR, GA and SA approaches. The GA and SA approaches evaluated proved to be a reliable optimization strategy for parameter estimation in Parana pine volumetric modelling, however, no significant differences were found in comparison with the NR approach. This study therefore contributes through the generation of robust equations that could be used for accurate estimates of the volume of the Parana pine in southern Brazil, thus supporting the planning and establishment of management and conservation actions.